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%I #15 Jan 22 2024 05:49:25
%S 20,8,27,164,98,345,343,222,555,590,1358,1388,1394,1407,1406,1419,
%T 3435,3231,3237,3236,3245,3243,3275,3282,3292,3297,8163,8361,8666,
%U 8662,8494,8493,8538,8590
%N a(n) is the least triprime T for which the Mertens function M(T) = n.
%H Jean-François Alcover, <a href="/A123174/b123174.txt">Table of n, a(n) for n = -3..100</a>
%F a(n) = min{T in A014612 and A002321(T) = n}.
%e a(-3) = 20 = 2^2 * 5 = the first triprime T for which the Mertens function M(T) = -3.
%e a(-2) = 8 = 2^3 = the first triprime T for which the Mertens function M(T) = -2.
%e a(-1) = 27 = 3^3 = the first triprime T for which the Mertens function M(T) = -1.
%e a(0) = 164 = 2^2 * 41 = min{A014612 INTERSECTION A028442} = the first triprime T for which the Mertens function M(T) = 0.
%e a(1) = 98 = 2 * 7^2 = min{A014612 INTERSECTION A118684} = the first triprime T for which the Mertens function M(T) = 1.
%e a(2) = 335 = 3 * 5 * 23 = the first triprime T for which the Mertens function M(T) = 2.
%e a(3) = 343 = 7^3 = the first triprime T for which the Mertens function M(T) = 3.
%p isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: A008683 := proc(n) option remember ; numtheory[mobius](n) ; end: A002321 := proc(n) option remember ; add(A008683(k),k=1..n) ; end: A123174 := proc(n) local T; for T from 2 do if isA014612(T) then if A002321(T) = n then RETURN(T) ; fi; fi; od: end: for n from -3 to 30 do printf("%d,",A123174(n)) ; od: # _R. J. Mathar_, Jan 27 2009
%t M[k_] := M[k] = MoebiusMu[Range[k]] // Total;
%t PO[k_] := PO[k] = PrimeOmega[k];
%t a[n_] := a[n] = Module[{k}, For[k = 8, True, k++, If[PO[k] == 3 && M[k] == n, Return[k]]]];
%t Table[Print[n, " ", a[n]]; a[n], {n, -3, 30}] (* _Jean-François Alcover_, Jan 22 2024 *)
%Y Cf. A002321, A014612, A028442, A118684.
%K easy,nonn
%O -3,1
%A _Jonathan Vos Post_, Oct 02 2006
%E a(2)=335 replaced with 345 and sequence extended to a(30) by _R. J. Mathar_, Jan 27 2009
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